We have previously reported (ECVP 2002) that errors of up to 40 in perceived direction of slant can be produced by rotation (“spin”) of an anisotropic surface texture in the plane of the slanted surface. Here we analyze the geometry of this situation, model our results, and present additional data in support of our model. Our anisotropic surface textures include a preponderance of contours oriented in one direction. When the surface is slanted, this anisotropy produces a projective gradient of convergence and a projective gradient of compression oriented at 90 to each other. The orientations of these gradients relative to the true direction of slant vary with the spin of the texture, but we show that these two gradients, taken together, are sufficient to mathematically specify the correct direction of slant for any spin angle. Observers are not able, however, to make consistent use of this information. Instead, there is a strong tendency to follow one or the other of these gradients rather than combining the information from both of them. We present a measure of the strength of each gradient, based on its rate of convergence or compression, and show analytically that the strengths of the two gradients vary reciprocally as a function of spin. We further show that we can accurately account for the modes of the error distributions, as the spin of the texture varies, with a model that bases judgments of direction of slant on the stronger of the two gradients, ignoring the other gradient. We measured observers' sensitivity to each of the two gradients as a function of spin and showed that observers were able to detect the direction of each gradient with a high degree of accuracy at all but the smallest spins. Thus our observers' performance is not due to the weaker gradient being too weak to detect, but is instead due to their failure, as indicated in our model, to incorporate information from the weaker gradient into their judgments of direction of slant.